THE LAW OF COSINES

WE USE THE LAW OF COSINES AND THE LAW OF SINES to solve triangles that are not right-angled. Such triangles are called oblique triangles. The Law of Cosines is used much more widely than the Law of Sines. Specifically, when we know two sides of a triangle and their included angle, then the Law of Cosines enables us to find the third side.

Thus if we know sides a and b and their included angle θ, then the Law of Cosines states:

c2 = a2 + b2 − 2ab cos θ

(The Law of Cosines is a extension of the Pythagorean theorem, because if θ were a right angle, we would have c2 = a2 + b2.)